%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE022+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:40:40 AM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 17 unt; 2 def)
% Number of atoms : 95 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 76 ( 33 ~; 28 |; 5 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 42 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f19,conjecture,
! [X0,X1] :
( test(X1)
=> ( leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))
& leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> ( leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))
& leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f22,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f29,plain,
? [X0,X1] :
( ( ~ leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))
| ~ leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0) )
& test(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f30,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f33,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f35,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f37,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f41,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f14]) ).
fof(f49,plain,
! [X0,X1] :
( ~ test(X0)
| complement(X0,X1)
| c(X0) != X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f53,plain,
( ~ leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1)
| ~ leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2)))) ),
inference(cnf_transformation,[],[f29]) ).
fof(f54,plain,
test(sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f55,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f49]) ).
fof(f56,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(consistent_polarity_flipping,[],[f41]) ).
fof(f59,plain,
! [X0] :
( complement(X0,c(X0))
| test(X0) ),
inference(consistent_polarity_flipping,[],[f55]) ).
fof(f64,plain,
~ test(sK2),
inference(consistent_polarity_flipping,[],[f54]) ).
fof(f65,plain,
( leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1)
| leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2)))) ),
inference(consistent_polarity_flipping,[],[f53]) ).
fof(f67,definition,
( spl3_1
<=> leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f69,plain,
( leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f71,definition,
( spl3_2
<=> leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f73,plain,
( leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f65,f71,f67]) ).
fof(f86,plain,
! [X0] :
( one = addition(c(X0),X0)
| test(X0) ),
inference(resolution,[],[f44,f59]) ).
fof(f87,plain,
! [X0] :
( test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f86,f30]) ).
fof(f146,plain,
( leq(multiplication(sK1,addition(sK2,c(sK2))),sK1)
| ~ spl3_2 ),
inference(superposition,[],[f73,f37]) ).
fof(f284,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f87,f64]) ).
fof(f295,plain,
( leq(multiplication(sK1,one),sK1)
| ~ spl3_2 ),
inference(superposition,[],[f146,f284]) ).
fof(f297,plain,
( leq(sK1,sK1)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f295,f35]) ).
fof(f298,plain,
( sK1 != addition(sK1,sK1)
| ~ spl3_2 ),
inference(resolution,[],[f297,f56]) ).
fof(f299,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f298,f33]) ).
fof(f300,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f299]) ).
fof(f301,plain,
( leq(sK1,multiplication(sK1,addition(sK2,c(sK2))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f69,f37]) ).
fof(f303,plain,
( leq(sK1,multiplication(sK1,one))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f301,f284]) ).
fof(f305,plain,
( leq(sK1,sK1)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f303,f35]) ).
fof(f307,plain,
( sK1 != addition(sK1,sK1)
| ~ spl3_1 ),
inference(resolution,[],[f305,f56]) ).
fof(f308,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f307,f33]) ).
fof(f309,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f308]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f74]) ).
cnf(s5,plain,
~ spl3_2,
inference(sat_conversion,[],[f300]) ).
cnf(s6,plain,
~ spl3_1,
inference(sat_conversion,[],[f309]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s5,s6]) ).
fof(f310,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE022+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 13:00:37 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.46 % (2962723)Will run a generic schedule for satisfiability detection.
% 0.10/0.46 % (2962729)% WARNING: option uhcvi not known.
% 0.10/0.46 % (2962729)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=663807755:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.46 % (2962733)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2284376909:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.46 % (2962728)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2377066756_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.46 % (2962730)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1728088224:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.46 % (2962731)dis+10_1_sil=32000:sp=arity:random_seed=3910955414:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.46 % (2962732)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=284205504:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.46 % (2962734)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=105838575:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.46 % TRYING [1]
% 0.10/0.46 % TRYING [2]
% 0.10/0.46 % (2962729) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2962723-2962729"...
% 0.10/0.46 % TRYING [3]
% 0.10/0.46 % (2962729)...printing done.
% 0.10/0.46 % (2962729)Refutation found. Thanks to Tanya!
% 0.10/0.46 % SZS status Theorem for theBenchmark
% 0.10/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.46 % (2962729)------------------------------
% 0.10/0.46 % (2962729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.46 % (2962729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.46 % (2962729)CaDiCaL version: 2.1.3
% 0.10/0.46 % (2962729)Termination reason: Refutation
% 0.10/0.46 % (2962729)Time elapsed: 0.005 s
% 0.10/0.46 % (2962729)Peak memory usage: 13 MB
% 0.10/0.46 % (2962729)Instructions burned: 12 (million)
% 0.10/0.46 % (2962723)Success in time 0.037 s
% 0.10/0.46 % Vampire exiting
%------------------------------------------------------------------------------